hard · GMAT Quant
A firm's average cost per unit at production volume x is C(x) = a + b/x, where a and b are positive constants. The firm observes C(20) = 18 and C(30) = 16. A total volume of 60 is split into two unequal positive-integer batches, with x denoting the smaller batch; x is even. A split is acceptable when the two batches' average costs differ by less than 2. The split must remain acceptable after 2 units are moved from the smaller batch to the larger batch.
What is the sum of all possible original values of x?
- 48
- 50
- 52
- 54
- 78
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